A study of combinatorial constructions and geometric characterizations of cubature formulas
Project/Area Number |
22740062
|
Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
Research Institution | Nagoya University |
Principal Investigator |
SAWA Masanori 名古屋大学, 情報科学研究科, 助教 (50508182)
|
Project Period (FY) |
2010 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | 求積公式 / デザイン / 直交多項式の零点 / 立体求積公式 / ユークリッドデザイン / 距離集合 / cubature / Euclidean design / Sobolevの定理 / Bajnokの定理 / 直交多項式 / 不変調和多項式 / 球面対称積分 / cubature formula / 最小cubature / Larman-Rogers-Seidelの定理 / Mysovskikh理論 |
Research Abstract |
We presented a number-theoretic characterization of the configuration of points of a minimal cubature formula, as well as some existence and non-existence results on such formulas of small degrees, by unifying techniques that have been developed in numerical analysis, algebraic combinatorics, discrete geometry and so on. We also characterize a minimal cubature formula whose point set consists of orbits of a finite irreducible reflection group.
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Report
(4 results)
Research Products
(44 results)